Question

A publisher reports that 69% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually over the reported percentage. A random sample of 200 found that 78% of the readers owned a particular make of car. Is there sufficient evidence at the 0.10 level to support the executive's claim?

Step 2 of 7 : Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 7 : Specify if the test is one-tailed or two-tailed.

Step 4 of 7 : Determine the P-value of the test statistic. Round your answer to four decimal places

Step 5 of 7 : Identify the value of the level of significance.

Step 6 of 7 : Make the decision to reject or fail to reject the null hypothesis.

Step 7 of 7 : State the conclusion of the hypothesis test.

Answer 1

The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H₀ : p = 0.69
H_A : p > 0.69

Hypothesis test results:

Proportion	Count	Total	Sample Prop.	Std. Err.	Z-Stat	P-value
p	156	200	0.78	0.032703211	2.7520234	0.003

Hence,

Step - 2: Test statistic = 2.75

Step - 3: This is a one tailed test since Ha contains > sign.

Step - 4: P - value = 0.003

Step - 5: Level of significance = 0.10

Step - 6: Reject the null hypothesis

Step - 7: Conclusion: There is sufficient evidence to support the marketing executive claim that the percentage is actually over the reported percentage.